Geometry Question

1. triangle QRS is isosceles, angles RQS and RSQ are equal. Let's call those angles y. Also angle PQS is 180-y. Not sufficient. Not enough info

2. triangle STU is isosceles, angles UST and SUT are equal. Let's call those angles z. Also angle SUP is 180-z. Not sufficient. Not enough info

1 and 2 together: we can put together 2 equations based on geometry principles:

x and the 2 angles adjacent add up to 180:

x+y+z = 180

the angles of the PQSU cuadrilateral add up to 360

90+x+PQS+SUP=360
or 90+x+(180-y)+(180-z)= 360

from x+y+z= 180, we get y=180-x-z, so

90+x+(180-(180-x-z))+(180-z)=360
90+x+(180-180+x+z) +(180-z)=360
90+x+180-180+x+z+180-z=360 (z's cancel out)
90+2x+180= 360
2x+270= 360
2x= 90
x=45

BOTH statements together are sufficient

note: there are 3 variables and 2 equations, this tempted me to choose E at first too, but you can solve due to cancelling out of terms...

hope i am right in my thinking

old geezer

QSR + x + UST = 180 (1)

RQS + QSR + PRT = 180 or
2QSR + PRT = 180 (2)

SUT + UST + PTR = 180 or
2UST + PTR = 180 (3)

PRT + PTR = 90 (4)

Ading (2) and (3):

2QSR + PRT + 2UST + PTR = 360
2(QSR + UST) = 360 - 90 = 270
QSR + UST = 135 (5)

From (1) and (5):
x + 135 = 180
x = 45